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Fix #2396 by removing redundant zero in IsNonAssociativeRing #2410

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Fix #2396 by removing redundant zero in IsNonAssociativeRing #2410

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ad622b2
Fix #2396 by removing redundant zero in IsNonAssociativeRing
lexvanderstoep Jun 16, 2024
07cae12
Remove zero arguments for IsNonAssociativeRing
lexvanderstoep Jun 16, 2024
83d9df2
Update CHANGELOG
lexvanderstoep Dec 21, 2024
83859b3
Fix whitespace
lexvanderstoep Dec 21, 2024
96f0f07
Merge branch 'master' into redundant_zero_proof
jamesmckinna Feb 6, 2025
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2 changes: 0 additions & 2 deletions src/Algebra/Construct/DirectProduct.agda
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Expand Up @@ -347,8 +347,6 @@ nonAssociativeRing R S = record
; *-identity = UnitalMagma.identity (unitalMagma R.*-unitalMagma S.*-unitalMagma)
; distrib = (λ x y z → (R.distribˡ , S.distribˡ) <*> x <*> y <*> z)
, (λ x y z → (R.distribʳ , S.distribʳ) <*> x <*> y <*> z)
; zero = uncurry (λ x y → R.zeroˡ x , S.zeroˡ y)
, uncurry (λ x y → R.zeroʳ x , S.zeroʳ y)
}

} where module R = NonAssociativeRing R; module S = NonAssociativeRing S
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16 changes: 9 additions & 7 deletions src/Algebra/Structures.agda
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Expand Up @@ -805,7 +805,6 @@ record IsNonAssociativeRing (+ * : Op₂ A) (-_ : Op₁ A) (0# 1# : A) : Set (a
*-cong : Congruent₂ *
*-identity : Identity 1# *
distrib : * DistributesOver +
zero : Zero 0# *

open IsAbelianGroup +-isAbelianGroup public
renaming
Expand Down Expand Up @@ -833,18 +832,21 @@ record IsNonAssociativeRing (+ * : Op₂ A) (-_ : Op₁ A) (0# 1# : A) : Set (a
; isGroup to +-isGroup
)

zeroˡ : LeftZero 0# *
zeroˡ = proj₁ zero

zeroʳ : RightZero 0# *
zeroʳ = proj₂ zero

distribˡ : * DistributesOverˡ +
distribˡ = proj₁ distrib

distribʳ : * DistributesOverʳ +
distribʳ = proj₂ distrib

zeroˡ : LeftZero 0# *
zeroˡ = Consequences.assoc∧distribʳ∧idʳ∧invʳ⇒zeˡ setoid +-cong *-cong +-assoc distribʳ +-identityʳ -‿inverseʳ

zeroʳ : RightZero 0# *
zeroʳ = Consequences.assoc∧distribˡ∧idʳ∧invʳ⇒zeʳ setoid +-cong *-cong +-assoc distribˡ +-identityʳ -‿inverseʳ

zero : Zero 0# *
zero = zeroˡ , zeroʳ

*-isMagma : IsMagma *
*-isMagma = record
{ isEquivalence = isEquivalence
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